A window through the walls of our classroom. This is an interactive learning ecology for students and parents in my Pre-Cal Math 20S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Wednesday, November 26, 2008

November 25, 2008 / Tuesday's Class

Yesterday we started the class of with finding the surface area and volume of each:

a. Sphere

To find the surface area of each sphere, you need to use the formula: 4pr²(p= pi)

Sphere 1:4p(1)² = 4p14x1xp = 4p

Sphere 2:4p(2)² = 4p44x4xp = 16p

Sphere 3:4p(3)² = 4p94x9xp = 36p

After doing this, you should notice a pattern or a relationship between the spheres above. The end result multiplied by pi have a perfect square in it. By noticing the pattern, you can jump to a sphere that has a radius of 10 instead of doing the formula one after another, after another and so on.For example, if your trying to find the volume of a sphere that has a radius of 10, I think you have to square the radius and then multiply it by 4, after doing that you multiply it by pi or leave it with the pi sign beside it as your final answer.*(This is where I personally feel lost, I am not sure how to explain it, hopefully this will help a little. I believe there is more to it, but this is where I am stuck.)*

Now you have to find the volume of each sphere using the formula: 4/3pr³(p= pi)

Sphere 1:4/3p(1)³ = 4/3p14x1xp divided by 3 = 4p/3

Sphere 2:4/3p(2)³ = 4/3p84x8xp divided by 3 = 32p/3

Sphere 3:4/2p(3)³ = 4/3p274x27xp divided by 3 = 108p/3

b. Cube

Now to find the surface area of each cube you have to use the formula: 6s²

Cube 1:6x1² = 6x1 = 6

Cube 2:6x2² = 6x4 = 24

Cube 3:6x3² = 6x9 = 54

I think there is another pattern, but I am not sure. I have no idea, so I'm just going to leave it as it is.

Now find the volume of each cube using the formula: lwhCube 1:1x1x1 = 1

Cube 2:2x2x2 = 8

Cube 33x3x3 = 27

Since the length, width and the height are all equal, there isn't much to do but to cube the length, width or height.

So most of the class was talking about these questions above and trying to look for a relationship or pattern between them and then we ended the class with sitting in groups trying to figure out these questions below:

1. The area of a shape is 30 cm². If the dimensions of the shape are increased 4 times, what is the area of the new shape?40 x 4² = 480 cm²

2. The volume of a solid is 24cm³. If the dimensions are tripled, what is the new volume?24 x 3³ = 648 cm³

Hopefully this scribe helps whoever did not understand the work we did yesterday, I know I got lost in some parts but I didn't say anything.